I would like to strongly recommend Xepha's Dynamic Weather (link [http://www.fallout3nexus.com/downloads/file.php?id=10607]) if you want a mod that adds weather and overhauls the lighting. I was using Fellout but I found some of its lighting changes to be too extreme (the lighting was often very bright during the day and too dark at night, and some lighting cycles looked quite unnatural in their colouring) and when I saw this [http://imgur.com/MgX1D] I was motivated to find a replacement.
The core feature of Xepha's Dynamic Weather is overhauled lighting effects which make the lighting vary more throughout the course of each day and depending on the weather, and also make the lighting look more natural. It also adds more detailed and more varied sky textures.
Additional weather like fog, rain, thunderstorms, and sandstorms are optional extras, there is an optional "green tint remover" which minimizes that faint, sickly green tone the lighting sometimes has, and you can also choose how dark you want the nights. By default, the nights vary from 'bright enough to see reasonably well' to 'too dark to navigate effectively' depending on the weather. Safe to say, they're a fair bit darker than vanilla. I personally like it this way.
I recommend these smaller mods to go with Dynamic Weather:
Megaton Lighting Overhaul
Ordinarily the lights in Megaton are just effects, they don't actually create any light on objects or the ground, that's handled by the ambient lighting. If you use any weather mod that makes nights darker, you should use this as well.
http://www.fallout3nexus.com/downloads/file.php?id=7875
Street Lights (DC Area)
This mod adds some environmental lights to the downtown DC area to make it easier to find your way at night.
http://www.fallout3nexus.com/downloads/file.php?id=8069
Street Lights (Wasteland)
An extension to the above, this adds some environmental lights to locations in the rest of the Wasteland.
http://www.fallout3nexus.com/downloads/file.php?id=10045
Decent Pip-boy Light
Doubles the range of the Pip-boy light so you can use it as a flashlight in dark areas, not just to look at things at arm's length.
http://www.fallout3nexus.com/downloads/file.php?id=778